The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated on three practical exercises that demonstrate advantages of the Monte Carlo approach in several parts of mathematics. The exercises are proposed for university courses but can be used also as an advanced application on secondary math school. The first example is focused on the classical use of the Monte Carlo method for calculating the area of polygons, the second and third examples are directed to the application of the Monte Carlo method for demonstrating the basic properties of different types of statistical estimations.